On Accelerating Monte Carlo Integration Using Orthogonal Projections

Autor:	Ming Hsuan Kang, Huei Wen Teng
Rok vydání:	2021
Předmět:	Statistics and Probability General Mathematics Monte Carlo method Orthographic projection Estimator Applied mathematics Asian option Monte Carlo integration Variance reduction Projection (linear algebra) Mathematics Probability measure
Zdroj:	Methodology and Computing in Applied Probability. 24:1143-1168
ISSN:	1573-7713 1387-5841
DOI:	10.1007/s11009-021-09893-3
Popis:	Monte Carlo simulation is an indispensable tool in calculating high-dimensional integrals. Although Monte Carlo integration is notoriously known for its slow convergence, it could be improved by various variance reduction techniques. This paper applies orthogonal projections to study the amount of variance reduction, and also proposes a novel projection estimator that is associated with a group of symmetries of the probability measure. For a given space of functions, the average variance reduction can be derived. For a specific function, its variance reduction is also analyzed. The well-known antithetic estimator is a special case of the projection estimator, and new results of its variance reduction and efficiency are provided. Various illustrations including pricing financial Asian options are provided to confirm our claims.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::c07030d0df288887aa2d45aa60784f85 https://doi.org/10.1007/s11009-021-09893-3 Zobrazit plný text záznamu Full text from SpringerLink